LMFDB - Embedded newform 1500.2.o.b.349.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(49,1500)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1500.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 5x^{14} + 6x^{12} - 20x^{10} - 79x^{8} - 80x^{6} + 96x^{4} + 320x^{2} + 256 $ x^16 + 5x^14 + 6x^12 - 20x^10 - 79x^8 - 80x^6 + 96x^4 + 320*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.2
Root			$-1.41395 - 0.0272949i$ of defining polynomial
Character	$\chi$	$=$	1500.349
Dual form			1500.2.o.b.649.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{3} +4.32440i q^{7} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{3} +4.32440i q^{7} +(-0.309017 + 0.951057i) q^{9} +(0.180557 + 0.555698i) q^{11} +(-0.918969 - 0.298591i) q^{13} +(-1.36625 + 1.88048i) q^{17} +(-4.35169 - 3.16169i) q^{19} +(3.49851 - 2.54182i) q^{21} +(-1.29166 + 0.419687i) q^{23} +(0.951057 - 0.309017i) q^{27} +(-0.571459 + 0.415189i) q^{29} +(-6.86707 - 4.98922i) q^{31} +(0.343440 - 0.472705i) q^{33} +(-5.81960 - 1.89090i) q^{37} +(0.298591 + 0.918969i) q^{39} +(3.41820 - 10.5201i) q^{41} +7.03076i q^{43} +(-5.33081 - 7.33723i) q^{47} -11.7004 q^{49} +2.32440 q^{51} +(5.23465 + 7.20487i) q^{53} +5.37899i q^{57} +(2.25351 - 6.93558i) q^{59} +(-1.48752 - 4.57810i) q^{61} +(-4.11275 - 1.33631i) q^{63} +(-0.221011 + 0.304195i) q^{67} +(1.09875 + 0.798291i) q^{69} +(-8.54359 + 6.20729i) q^{71} +(0.202931 - 0.0659364i) q^{73} +(-2.40306 + 0.780801i) q^{77} +(-5.68410 + 4.12974i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-9.46998 + 13.0343i) q^{83} +(0.671790 + 0.218278i) q^{87} +(4.33233 + 13.3335i) q^{89} +(1.29123 - 3.97399i) q^{91} +8.48817i q^{93} +(-9.25880 - 12.7436i) q^{97} -0.584296 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^9	$ 16 q + 4 q^{9} + 16 q^{11} - 10 q^{19} + 14 q^{21} + 6 q^{29} - 6 q^{31} + 20 q^{41} + 16 q^{49} - 16 q^{51} + 76 q^{59} + 92 q^{61} - 4 q^{69} - 50 q^{71} + 32 q^{79} - 4 q^{81} + 60 q^{89} + 50 q^{91} + 4 q^{99}+O(q^{100}) $ 16 * q + 4 * q^9 + 16 * q^11 - 10 * q^19 + 14 * q^21 + 6 * q^29 - 6 * q^31 + 20 * q^41 + 16 * q^49 - 16 * q^51 + 76 * q^59 + 92 * q^61 - 4 * q^69 - 50 * q^71 + 32 * q^79 - 4 * q^81 + 60 * q^89 + 50 * q^91 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			4.32440i			1.63447i	0.576306	+	0.817234i	$0.304494\pi$
$7$			4.32440i			1.63447i	−0.576306	+	0.817234i	$0.695506\pi$
$8$		0			0
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$		0			0
$11$	0.180557	+	0.555698i	0.0544401	+	0.167549i	0.974580	−	0.224041i	$-0.0719250\pi$
$11$	0.180557	+	0.555698i	0.0544401	+	0.167549i	−0.920140	+	0.391590i	$0.871925\pi$
$12$		0			0
$13$	−0.918969	−	0.298591i	−0.254876	−	0.0828143i	0.178792	−	0.983887i	$-0.442781\pi$
$13$	−0.918969	−	0.298591i	−0.254876	−	0.0828143i	−0.433668	+	0.901073i	$0.642781\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.36625	+	1.88048i	−0.331363	+	0.456082i	−0.941894	−	0.335910i	$-0.890956\pi$
$17$	−1.36625	+	1.88048i	−0.331363	+	0.456082i	0.610531	+	0.791993i	$0.290956\pi$
$18$		0			0
$19$	−4.35169	−	3.16169i	−0.998346	−	0.725341i	−0.0366134	−	0.999330i	$-0.511657\pi$
$19$	−4.35169	−	3.16169i	−0.998346	−	0.725341i	−0.961733	+	0.273988i	$0.911657\pi$
$20$		0			0
$21$	3.49851	−	2.54182i	0.763437	−	0.554670i
$22$		0			0
$23$	−1.29166	+	0.419687i	−0.269330	+	0.0875107i	−0.440569	−	0.897719i	$-0.645223\pi$
$23$	−1.29166	+	0.419687i	−0.269330	+	0.0875107i	0.171238	+	0.985230i	$0.445223\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$		0			0
$29$	−0.571459	+	0.415189i	−0.106117	+	0.0770987i	−0.639578	−	0.768726i	$-0.720891\pi$
$29$	−0.571459	+	0.415189i	−0.106117	+	0.0770987i	0.533461	+	0.845825i	$0.320891\pi$
$30$		0			0
$31$	−6.86707	−	4.98922i	−1.23336	−	0.896090i	−0.236225	−	0.971698i	$-0.575910\pi$
$31$	−6.86707	−	4.98922i	−1.23336	−	0.896090i	−0.997138	+	0.0756084i	$0.975910\pi$
$32$		0			0
$33$	0.343440	−	0.472705i	0.0597853	−	0.0822874i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.81960	−	1.89090i	−0.956736	−	0.310862i	−0.211286	−	0.977424i	$-0.567765\pi$
$37$	−5.81960	−	1.89090i	−0.956736	−	0.310862i	−0.745450	+	0.666562i	$0.767765\pi$
$38$		0			0
$39$	0.298591	+	0.918969i	0.0478129	+	0.147153i
$40$		0			0
$41$	3.41820	−	10.5201i	0.533833	−	1.64297i	−0.212325	−	0.977199i	$-0.568104\pi$
$41$	3.41820	−	10.5201i	0.533833	−	1.64297i	0.746158	−	0.665769i	$-0.231896\pi$
$42$		0			0
$43$			7.03076i			1.07218i	0.844161	+	0.536090i	$0.180099\pi$
$43$			7.03076i			1.07218i	−0.844161	+	0.536090i	$0.819901\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.33081	−	7.33723i	−0.777579	−	1.07025i	−0.995545	−	0.0942890i	$-0.969942\pi$
$47$	−5.33081	−	7.33723i	−0.777579	−	1.07025i	0.217966	−	0.975956i	$-0.430058\pi$
$48$		0			0
$49$	−11.7004			−1.67149
$50$		0			0
$51$	2.32440			0.325481
$52$		0			0
$53$	5.23465	+	7.20487i	0.719034	+	0.989665i	0.999555	+	0.0298175i	$0.00949262\pi$
$53$	5.23465	+	7.20487i	0.719034	+	0.989665i	−0.280521	+	0.959848i	$0.590507\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			5.37899i			0.712464i
$58$		0			0
$59$	2.25351	−	6.93558i	0.293382	−	0.902936i	−0.690379	−	0.723448i	$-0.742556\pi$
$59$	2.25351	−	6.93558i	0.293382	−	0.902936i	0.983760	−	0.179487i	$-0.0574439\pi$
$60$		0			0
$61$	−1.48752	−	4.57810i	−0.190457	−	0.586166i	0.809543	−	0.587061i	$-0.199715\pi$
$61$	−1.48752	−	4.57810i	−0.190457	−	0.586166i	−1.00000		0.000895115i	$0.999715\pi$
$62$		0			0
$63$	−4.11275	−	1.33631i	−0.518157	−	0.168359i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.221011	+	0.304195i	−0.0270008	+	0.0371634i	−0.822304	−	0.569049i	$-0.807312\pi$
$67$	−0.221011	+	0.304195i	−0.0270008	+	0.0371634i	0.795303	+	0.606212i	$0.207312\pi$
$68$		0			0
$69$	1.09875	+	0.798291i	0.132274	+	0.0961030i
$70$		0			0
$71$	−8.54359	+	6.20729i	−1.01394	+	0.736669i	−0.965031	−	0.262134i	$-0.915574\pi$
$71$	−8.54359	+	6.20729i	−1.01394	+	0.736669i	−0.0489067	+	0.998803i	$0.515574\pi$
$72$		0			0
$73$	0.202931	−	0.0659364i	0.0237513	−	0.00771727i	−0.297117	−	0.954841i	$-0.596025\pi$
$73$	0.202931	−	0.0659364i	0.0237513	−	0.00771727i	0.320869	+	0.947124i	$0.396025\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.40306	+	0.780801i	−0.273854	+	0.0889806i
$78$		0			0
$79$	−5.68410	+	4.12974i	−0.639511	+	0.464632i	−0.859682	−	0.510829i	$-0.829339\pi$
$79$	−5.68410	+	4.12974i	−0.639511	+	0.464632i	0.220171	+	0.975461i	$0.429339\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	−9.46998	+	13.0343i	−1.03946	+	1.43070i	−0.141867	+	0.989886i	$0.545310\pi$
$83$	−9.46998	+	13.0343i	−1.03946	+	1.43070i	−0.897598	+	0.440815i	$0.854690\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.671790	+	0.218278i	0.0720235	+	0.0234018i
$88$		0			0
$89$	4.33233	+	13.3335i	0.459226	+	1.41335i	0.866101	+	0.499869i	$0.166618\pi$
$89$	4.33233	+	13.3335i	0.459226	+	1.41335i	−0.406875	+	0.913484i	$0.633382\pi$
$90$		0			0
$91$	1.29123	−	3.97399i	0.135357	−	0.416587i
$92$		0			0
$93$			8.48817i			0.880182i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−9.25880	−	12.7436i	−0.940089	−	1.29392i	−0.955792	−	0.294044i	$-0.904999\pi$
$97$	−9.25880	−	12.7436i	−0.940089	−	1.29392i	0.0157030	−	0.999877i	$-0.495001\pi$
$98$		0			0
$99$	−0.584296			−0.0587239
$100$		0			0
$101$	7.14178			0.710634			0.355317	−	0.934746i	$-0.384373\pi$
$101$	7.14178			0.710634			0.355317	+	0.934746i	$0.384373\pi$
$102$		0			0
$103$	0.779130	+	1.07238i	0.0767699	+	0.105665i	0.845675	−	0.533698i	$-0.179198\pi$
$103$	0.779130	+	1.07238i	0.0767699	+	0.105665i	−0.768905	+	0.639363i	$0.779198\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			17.6796i			1.70915i	0.519331	+	0.854573i	$0.326181\pi$
$107$			17.6796i			1.70915i	−0.519331	+	0.854573i	$0.673819\pi$
$108$		0			0
$109$	−1.09385	+	3.36653i	−0.104772	+	0.322455i	−0.989677	−	0.143317i	$-0.954223\pi$
$109$	−1.09385	+	3.36653i	−0.104772	+	0.322455i	0.884905	+	0.465772i	$0.154223\pi$
$110$		0			0
$111$	1.89090	+	5.81960i	0.179476	+	0.552372i
$112$		0			0
$113$	−16.6322	−	5.40414i	−1.56463	−	0.508379i	−0.606590	−	0.795015i	$-0.707463\pi$
$113$	−16.6322	−	5.40414i	−1.56463	−	0.508379i	−0.958039	+	0.286636i	$0.907463\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.567954	−	0.781722i	0.0525074	−	0.0722702i
$118$		0			0
$119$	−8.13192	−	5.90819i	−0.745452	−	0.541603i
$120$		0			0
$121$	8.62299	−	6.26497i	0.783908	−	0.569542i
$122$		0			0
$123$	−10.5201	+	3.41820i	−0.948568	+	0.308208i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−16.6492	+	5.40966i	−1.47738	+	0.480030i	−0.933329	−	0.359022i	$-0.883110\pi$
$127$	−16.6492	+	5.40966i	−1.47738	+	0.480030i	−0.544051	+	0.839052i	$0.683110\pi$
$128$		0			0
$129$	5.68800	−	4.13258i	0.500801	−	0.363853i
$130$		0			0
$131$	15.2629	+	11.0892i	1.33353	+	0.968865i	0.999656	+	0.0262465i	$0.00835549\pi$
$131$	15.2629	+	11.0892i	1.33353	+	0.968865i	0.333872	+	0.942618i	$0.391645\pi$
$132$		0			0
$133$	13.6724	−	18.8184i	1.18555	−	1.63177i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	12.6023	+	4.09472i	1.07668	+	0.349836i	0.793087	−	0.609108i	$-0.208472\pi$
$137$	12.6023	+	4.09472i	1.07668	+	0.349836i	0.283596	+	0.958944i	$0.408472\pi$
$138$		0			0
$139$	5.22318	+	16.0753i	0.443024	+	1.36349i	0.884636	+	0.466283i	$0.154407\pi$
$139$	5.22318	+	16.0753i	0.443024	+	1.36349i	−0.441611	+	0.897206i	$0.645593\pi$
$140$		0			0
$141$	−2.80257	+	8.62543i	−0.236019	+	0.726393i
$142$		0			0
$143$		−	0.564582i		−	0.0472128i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.87732	+	9.46582i	0.567232	+	0.780728i
$148$		0			0
$149$	−12.1625			−0.996388			−0.498194	−	0.867066i	$-0.666003\pi$
$149$	−12.1625			−0.996388			−0.498194	+	0.867066i	$0.666003\pi$
$150$		0			0
$151$	−9.84446			−0.801131			−0.400565	−	0.916268i	$-0.631186\pi$
$151$	−9.84446			−0.801131			−0.400565	+	0.916268i	$0.631186\pi$
$152$		0			0
$153$	−1.36625	−	1.88048i	−0.110454	−	0.152027i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	18.4804i		−	1.47489i	−0.675405	−	0.737447i	$-0.736031\pi$
$157$		−	18.4804i		−	1.47489i	0.675405	−	0.737447i	$-0.263969\pi$
$158$		0			0
$159$	2.75202	−	8.46984i	0.218249	−	0.671702i
$160$		0			0
$161$	−1.81489	−	5.58566i	−0.143033	−	0.440212i
$162$		0			0
$163$	13.8253	+	4.49212i	1.08288	+	0.351850i	0.795492	−	0.605964i	$-0.207212\pi$
$163$	13.8253	+	4.49212i	1.08288	+	0.351850i	0.287390	+	0.957814i	$0.407212\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.64091	+	3.63490i	−0.204360	+	0.281277i	−0.898879	−	0.438197i	$-0.855617\pi$
$167$	−2.64091	+	3.63490i	−0.204360	+	0.281277i	0.694519	+	0.719474i	$0.255617\pi$
$168$		0			0
$169$	−9.76187	−	7.09242i	−0.750913	−	0.545570i
$170$		0			0
$171$	4.35169	−	3.16169i	0.332782	−	0.241780i
$172$		0			0
$173$	1.90036	−	0.617465i	0.144482	−	0.0469450i	−0.235883	−	0.971781i	$-0.575798\pi$
$173$	1.90036	−	0.617465i	0.144482	−	0.0469450i	0.380365	+	0.924836i	$0.375798\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−6.93558	+	2.25351i	−0.521310	+	0.169384i
$178$		0			0
$179$	11.3095	−	8.21683i	0.845312	−	0.614155i	−0.0785376	−	0.996911i	$-0.525025\pi$
$179$	11.3095	−	8.21683i	0.845312	−	0.614155i	0.923849	+	0.382756i	$0.125025\pi$
$180$		0			0
$181$	−10.9524	−	7.95740i	−0.814087	−	0.591469i	0.100926	−	0.994894i	$-0.467820\pi$
$181$	−10.9524	−	7.95740i	−0.814087	−	0.591469i	−0.915013	+	0.403425i	$0.867820\pi$
$182$		0			0
$183$	−2.82942	+	3.89437i	−0.209157	+	0.287880i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.29166	−	0.419687i	−0.0944557	−	0.0306905i
$188$		0			0
$189$	1.33631	+	4.11275i	0.0972024	+	0.299158i
$190$		0			0
$191$	0.786594	−	2.42089i	0.0569160	−	0.175169i	−0.918557	−	0.395288i	$-0.870645\pi$
$191$	0.786594	−	2.42089i	0.0569160	−	0.175169i	0.975473	+	0.220119i	$0.0706446\pi$
$192$		0			0
$193$		−	5.60541i		−	0.403486i	−0.979438	−	0.201743i	$-0.935339\pi$
$193$		−	5.60541i		−	0.403486i	0.979438	−	0.201743i	$-0.0646606\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.61776	+	6.35580i	0.329002	+	0.452832i	0.941189	−	0.337881i	$-0.109710\pi$
$197$	4.61776	+	6.35580i	0.329002	+	0.452832i	−0.612187	+	0.790713i	$0.709710\pi$
$198$		0			0
$199$	−16.9970			−1.20489			−0.602443	−	0.798162i	$-0.705806\pi$
$199$	−16.9970			−1.20489			−0.602443	+	0.798162i	$0.705806\pi$
$200$		0			0
$201$	0.376006			0.0265214
$202$		0			0
$203$	−1.79544	−	2.47122i	−0.126015	−	0.173445i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	1.35813i		−	0.0943969i
$208$		0			0
$209$	0.971215	−	2.98909i	0.0671804	−	0.206760i
$210$		0			0
$211$	−4.00341	−	12.3212i	−0.275606	−	0.848229i	−0.989058	−	0.147525i	$-0.952869\pi$
$211$	−4.00341	−	12.3212i	−0.275606	−	0.848229i	0.713452	−	0.700704i	$-0.247131\pi$
$212$		0			0
$213$	10.0436	+	3.26336i	0.688176	+	0.223602i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	21.5754	−	29.6959i	1.46463	−	2.01589i
$218$		0			0
$219$	−0.172624	−	0.125419i	−0.0116648	−	0.00847500i
$220$		0			0
$221$	1.81703	−	1.32015i	0.122227	−	0.0888030i
$222$		0			0
$223$	18.0512	−	5.86518i	1.20880	−	0.392761i	0.365806	−	0.930691i	$-0.380793\pi$
$223$	18.0512	−	5.86518i	1.20880	−	0.392761i	0.842990	+	0.537930i	$0.180793\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.366260	−	0.119005i	0.0243095	−	0.00789865i	−0.296837	−	0.954928i	$-0.595932\pi$
$227$	0.366260	−	0.119005i	0.0243095	−	0.00789865i	0.321147	+	0.947030i	$0.395932\pi$
$228$		0			0
$229$	8.30740	−	6.03568i	0.548968	−	0.398849i	−0.278437	−	0.960455i	$-0.589816\pi$
$229$	8.30740	−	6.03568i	0.548968	−	0.398849i	0.827405	+	0.561606i	$0.189816\pi$
$230$		0			0
$231$	2.04416	+	1.48517i	0.134496	+	0.0977172i
$232$		0			0
$233$	12.7185	−	17.5055i	0.833217	−	1.14682i	−0.154099	−	0.988055i	$-0.549247\pi$
$233$	12.7185	−	17.5055i	0.833217	−	1.14682i	0.987316	−	0.158769i	$-0.0507526\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	6.68206	+	2.17113i	0.434047	+	0.141030i
$238$		0			0
$239$	2.38438	+	7.33836i	0.154233	+	0.474679i	0.998082	−	0.0619006i	$-0.0197162\pi$
$239$	2.38438	+	7.33836i	0.154233	+	0.474679i	−0.843850	+	0.536579i	$0.819716\pi$
$240$		0			0
$241$	−7.82629	+	24.0868i	−0.504136	+	1.55157i	0.298083	+	0.954540i	$0.403653\pi$
$241$	−7.82629	+	24.0868i	−0.504136	+	1.55157i	−0.802219	+	0.597030i	$0.796347\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.05502	+	4.20487i	0.194386	+	0.267550i
$248$		0			0
$249$	16.1113			1.02101
$250$		0			0
$251$	−2.39913			−0.151432			−0.0757160	−	0.997129i	$-0.524124\pi$
$251$	−2.39913			−0.151432			−0.0757160	+	0.997129i	$0.524124\pi$
$252$		0			0
$253$	−0.466438	−	0.641997i	−0.0293247	−	0.0403620i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	14.3086i		−	0.892548i	−0.894896	−	0.446274i	$-0.852751\pi$
$257$		−	14.3086i		−	0.892548i	0.894896	−	0.446274i	$-0.147249\pi$
$258$		0			0
$259$	8.17701	−	25.1662i	0.508095	−	1.56375i
$260$		0			0
$261$	−0.218278	−	0.671790i	−0.0135111	−	0.0415828i
$262$		0			0
$263$	−12.4403	−	4.04210i	−0.767103	−	0.249247i	−0.100779	−	0.994909i	$-0.532133\pi$
$263$	−12.4403	−	4.04210i	−0.767103	−	0.249247i	−0.666324	+	0.745662i	$0.732133\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	8.24058	−	11.3422i	0.504315	−	0.694131i
$268$		0			0
$269$	24.8165	+	18.0302i	1.51309	+	1.09932i	0.964783	+	0.263046i	$0.0847270\pi$
$269$	24.8165	+	18.0302i	1.51309	+	1.09932i	0.548306	+	0.836278i	$0.315273\pi$
$270$		0			0
$271$	−11.5174	+	8.36785i	−0.699629	+	0.508310i	−0.879811	−	0.475323i	$-0.842331\pi$
$271$	−11.5174	+	8.36785i	−0.699629	+	0.508310i	0.180182	+	0.983633i	$0.442331\pi$
$272$		0			0
$273$	−3.97399	+	1.29123i	−0.240517	+	0.0781486i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−19.1454	+	6.22072i	−1.15034	+	0.373767i	−0.821270	−	0.570540i	$-0.806734\pi$
$277$	−19.1454	+	6.22072i	−1.15034	+	0.373767i	−0.329066	+	0.944307i	$0.606734\pi$
$278$		0			0
$279$	6.86707	−	4.98922i	0.411121	−	0.298697i
$280$		0			0
$281$	7.94172	+	5.77000i	0.473763	+	0.344209i	0.798906	−	0.601456i	$-0.205412\pi$
$281$	7.94172	+	5.77000i	0.473763	+	0.344209i	−0.325143	+	0.945665i	$0.605412\pi$
$282$		0			0
$283$	−3.84733	+	5.29540i	−0.228700	+	0.314779i	−0.907910	−	0.419166i	$-0.862323\pi$
$283$	−3.84733	+	5.29540i	−0.228700	+	0.314779i	0.679210	+	0.733944i	$0.262323\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	45.4932	+	14.7816i	2.68538	+	0.872532i
$288$		0			0
$289$	3.58373	+	11.0296i	0.210807	+	0.648799i
$290$		0			0
$291$	−4.86764	+	14.9811i	−0.285346	+	0.878205i
$292$		0			0
$293$		−	0.869428i		−	0.0507925i	−0.999677	−	0.0253963i	$-0.991915\pi$
$293$		−	0.869428i		−	0.0507925i	0.999677	−	0.0253963i	$-0.00808475\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.343440	+	0.472705i	0.0199284	+	0.0274291i
$298$		0			0
$299$	1.31231			0.0758930
$300$		0			0
$301$	−30.4038			−1.75244
$302$		0			0
$303$	−4.19783	−	5.77782i	−0.241159	−	0.331927i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			21.7261i			1.23997i	0.784613	+	0.619986i	$0.212862\pi$
$307$			21.7261i			1.23997i	−0.784613	+	0.619986i	$0.787138\pi$
$308$		0			0
$309$	0.409613	−	1.26066i	0.0233021	−	0.0717163i
$310$		0			0
$311$	5.86610	+	18.0540i	0.332636	+	1.02375i	0.967875	+	0.251432i	$0.0809016\pi$
$311$	5.86610	+	18.0540i	0.332636	+	1.02375i	−0.635239	+	0.772316i	$0.719098\pi$
$312$		0			0
$313$	5.78443	+	1.87947i	0.326955	+	0.106234i	0.467895	−	0.883784i	$-0.345012\pi$
$313$	5.78443	+	1.87947i	0.326955	+	0.106234i	−0.140940	+	0.990018i	$0.545012\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.16274	−	1.60038i	0.0653060	−	0.0898860i	−0.775115	−	0.631821i	$-0.782308\pi$
$317$	1.16274	−	1.60038i	0.0653060	−	0.0898860i	0.840421	+	0.541935i	$0.182308\pi$
$318$		0			0
$319$	−0.333901	−	0.242593i	−0.0186949	−	0.0135826i
$320$		0			0
$321$	14.3031	−	10.3918i	0.798319	−	0.580013i
$322$		0			0
$323$	11.8910	−	3.86361i	0.661631	−	0.214977i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.36653	−	1.09385i	0.186169	−	0.0604901i
$328$		0			0
$329$	31.7291	−	23.0525i	1.74928	−	1.27093i
$330$		0			0
$331$	10.6230	+	7.71805i	0.583892	+	0.424223i	0.840125	−	0.542393i	$-0.182481\pi$
$331$	10.6230	+	7.71805i	0.583892	+	0.424223i	−0.256233	+	0.966615i	$0.582481\pi$
$332$		0			0
$333$	3.59671	−	4.95044i	0.197098	−	0.271283i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	10.9333	+	3.55245i	0.595576	+	0.193514i	0.591266	−	0.806476i	$-0.298628\pi$
$337$	10.9333	+	3.55245i	0.595576	+	0.193514i	0.00430942	+	0.999991i	$0.498628\pi$
$338$		0			0
$339$	5.40414	+	16.6322i	0.293513	+	0.903339i
$340$		0			0
$341$	1.53260	−	4.71686i	0.0829949	−	0.255432i
$342$		0			0
$343$		−	20.3264i		−	1.09752i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.5028	−	24.0905i	−0.939599	−	1.29325i	−0.955995	−	0.293381i	$-0.905219\pi$
$347$	−17.5028	−	24.0905i	−0.939599	−	1.29325i	0.0163966	−	0.999866i	$-0.494781\pi$
$348$		0			0
$349$	−10.0870			−0.539946			−0.269973	−	0.962868i	$-0.587015\pi$
$349$	−10.0870			−0.539946			−0.269973	+	0.962868i	$0.587015\pi$
$350$		0			0
$351$	−0.966262			−0.0515752
$352$		0			0
$353$	−8.38300	−	11.5382i	−0.446182	−	0.614117i	0.525390	−	0.850862i	$-0.323919\pi$
$353$	−8.38300	−	11.5382i	−0.446182	−	0.614117i	−0.971572	+	0.236745i	$0.923919\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			10.0516i			0.531988i
$358$		0			0
$359$	2.04232	−	6.28562i	0.107790	−	0.331742i	−0.882585	−	0.470152i	$-0.844199\pi$
$359$	2.04232	−	6.28562i	0.107790	−	0.331742i	0.990375	+	0.138410i	$0.0441991\pi$
$360$		0			0
$361$	3.06962	+	9.44731i	0.161559	+	0.497227i
$362$		0			0
$363$	−10.1369	−	3.29369i	−0.532051	−	0.172874i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	5.60900	−	7.72012i	0.292787	−	0.402987i	−0.637130	−	0.770757i	$-0.719878\pi$
$367$	5.60900	−	7.72012i	0.292787	−	0.402987i	0.929917	+	0.367770i	$0.119878\pi$
$368$		0			0
$369$	8.94895	+	6.50180i	0.465864	+	0.338470i
$370$		0			0
$371$	−31.1567	+	22.6367i	−1.61758	+	1.17524i
$372$		0			0
$373$	−1.23959	+	0.402767i	−0.0641835	+	0.0208545i	−0.340933	−	0.940088i	$-0.610743\pi$
$373$	−1.23959	+	0.402767i	−0.0641835	+	0.0208545i	0.276749	+	0.960942i	$0.410743\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.649125	−	0.210914i	0.0334317	−	0.0108626i
$378$		0			0
$379$	19.6474	−	14.2747i	1.00922	−	0.733240i	0.0451733	−	0.998979i	$-0.485616\pi$
$379$	19.6474	−	14.2747i	1.00922	−	0.733240i	0.964045	+	0.265739i	$0.0856160\pi$
$380$		0			0
$381$	14.1627	+	10.2898i	0.725576	+	0.527162i
$382$		0			0
$383$	−7.13094	+	9.81489i	−0.364374	+	0.501518i	−0.951361	−	0.308079i	$-0.900314\pi$
$383$	−7.13094	+	9.81489i	−0.364374	+	0.501518i	0.586987	+	0.809596i	$0.300314\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−6.68665	−	2.17262i	−0.339901	−	0.110441i
$388$		0			0
$389$	9.04178	+	27.8278i	0.458437	+	1.41092i	0.867053	+	0.498217i	$0.166012\pi$
$389$	9.04178	+	27.8278i	0.458437	+	1.41092i	−0.408616	+	0.912706i	$0.633988\pi$
$390$		0			0
$391$	0.975518	−	3.00234i	0.0493341	−	0.151835i
$392$		0			0
$393$		−	18.8660i		−	0.951664i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−3.69940	−	5.09179i	−0.185668	−	0.255550i	0.706029	−	0.708183i	$-0.250485\pi$
$397$	−3.69940	−	5.09179i	−0.185668	−	0.255550i	−0.891697	+	0.452633i	$0.850485\pi$
$398$		0			0
$399$	−23.2609			−1.16450
$400$		0			0
$401$	30.3064			1.51343			0.756714	−	0.653747i	$-0.226804\pi$
$401$	30.3064			1.51343			0.756714	+	0.653747i	$0.226804\pi$
$402$		0			0
$403$	4.82089	+	6.63539i	0.240146	+	0.330532i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	3.57536i		−	0.177224i
$408$		0			0
$409$	−5.70942	+	17.5718i	−0.282313	+	0.868870i	0.704878	+	0.709328i	$0.251002\pi$
$409$	−5.70942	+	17.5718i	−0.282313	+	0.868870i	−0.987191	+	0.159541i	$0.948998\pi$
$410$		0			0
$411$	−4.09472	−	12.6023i	−0.201978	−	0.621623i
$412$		0			0
$413$	29.9922	+	9.74505i	1.47582	+	0.479523i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	9.93508	−	13.6745i	0.486523	−	0.669641i
$418$		0			0
$419$	−18.1586	−	13.1930i	−0.887108	−	0.644522i	0.0480143	−	0.998847i	$-0.484711\pi$
$419$	−18.1586	−	13.1930i	−0.887108	−	0.644522i	−0.935122	+	0.354325i	$0.884711\pi$
$420$		0			0
$421$	5.05679	−	3.67397i	0.246453	−	0.179058i	−0.457700	−	0.889106i	$-0.651327\pi$
$421$	5.05679	−	3.67397i	0.246453	−	0.179058i	0.704153	+	0.710048i	$0.251327\pi$
$422$		0			0
$423$	8.62543	−	2.80257i	0.419383	−	0.136266i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	19.7975	−	6.43260i	0.958069	−	0.311296i
$428$		0			0
$429$	−0.456757	+	0.331853i	−0.0220524	+	0.0160220i
$430$		0			0
$431$	−27.9850	−	20.3323i	−1.34799	−	0.979373i	−0.999109	−	0.0422061i	$-0.986561\pi$
$431$	−27.9850	−	20.3323i	−1.34799	−	0.979373i	−0.348882	−	0.937167i	$-0.613439\pi$
$432$		0			0
$433$	2.31081	−	3.18056i	0.111050	−	0.152848i	−0.749874	−	0.661581i	$-0.769886\pi$
$433$	2.31081	−	3.18056i	0.111050	−	0.152848i	0.860924	+	0.508733i	$0.169886\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.94784	+	2.25749i	0.332360	+	0.107990i
$438$		0			0
$439$	−1.54170	−	4.74487i	−0.0735815	−	0.226460i	0.907501	−	0.420049i	$-0.137987\pi$
$439$	−1.54170	−	4.74487i	−0.0735815	−	0.226460i	−0.981083	+	0.193589i	$0.937987\pi$
$440$		0			0
$441$	3.61562	−	11.1277i	0.172173	−	0.529893i
$442$		0			0
$443$		−	9.92754i		−	0.471672i	−0.971793	−	0.235836i	$-0.924217\pi$
$443$		−	9.92754i		−	0.471672i	0.971793	−	0.235836i	$-0.0757828\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	7.14892	+	9.83964i	0.338132	+	0.465399i
$448$		0			0
$449$	−9.87365			−0.465966			−0.232983	−	0.972481i	$-0.574849\pi$
$449$	−9.87365			−0.465966			−0.232983	+	0.972481i	$0.574849\pi$
$450$		0			0
$451$	6.46320			0.304340
$452$		0			0
$453$	5.78643	+	7.96433i	0.271870	+	0.374197i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			12.6424i			0.591387i	0.955283	+	0.295693i	$0.0955507\pi$
$457$			12.6424i			0.591387i	−0.955283	+	0.295693i	$0.904449\pi$
$458$		0			0
$459$	−0.718278	+	2.21063i	−0.0335263	+	0.103183i
$460$		0			0
$461$	12.2911	+	37.8280i	0.572452	+	1.76183i	0.644697	+	0.764438i	$0.276984\pi$
$461$	12.2911	+	37.8280i	0.572452	+	1.76183i	−0.0722451	+	0.997387i	$0.523016\pi$
$462$		0			0
$463$	−4.20242	−	1.36545i	−0.195303	−	0.0634578i	0.209732	−	0.977759i	$-0.432741\pi$
$463$	−4.20242	−	1.36545i	−0.195303	−	0.0634578i	−0.405035	+	0.914301i	$0.632741\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.62706	+	9.12137i	−0.306664	+	0.422086i	−0.934337	−	0.356390i	$-0.884007\pi$
$467$	−6.62706	+	9.12137i	−0.306664	+	0.422086i	0.627673	+	0.778477i	$0.284007\pi$
$468$		0			0
$469$	−1.31546	−	0.955738i	−0.0607423	−	0.0441319i
$470$		0			0
$471$	−14.9509	+	10.8625i	−0.688902	+	0.500517i
$472$		0			0
$473$	−3.90698	+	1.26945i	−0.179643	+	0.0583696i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−8.46984	+	2.75202i	−0.387807	+	0.126006i
$478$		0			0
$479$	−4.49728	+	3.26747i	−0.205486	+	0.149294i	−0.685769	−	0.727819i	$-0.740534\pi$
$479$	−4.49728	+	3.26747i	−0.205486	+	0.149294i	0.480283	+	0.877114i	$0.340534\pi$
$480$		0			0
$481$	4.78343	+	3.47536i	0.218105	+	0.158463i
$482$		0			0
$483$	−3.45213	+	4.75145i	−0.157077	+	0.216198i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−15.8199	−	5.14021i	−0.716870	−	0.232925i	−0.0722042	−	0.997390i	$-0.523003\pi$
$487$	−15.8199	−	5.14021i	−0.716870	−	0.232925i	−0.644665	+	0.764465i	$0.723003\pi$
$488$		0			0
$489$	−4.49212	−	13.8253i	−0.203141	−	0.625202i
$490$		0			0
$491$	0.327326	−	1.00741i	0.0147720	−	0.0454636i	−0.943399	−	0.331661i	$-0.892391\pi$
$491$	0.327326	−	1.00741i	0.0147720	−	0.0454636i	0.958171	+	0.286197i	$0.0923912\pi$
$492$		0			0
$493$		−	1.64187i		−	0.0739459i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−26.8428	−	36.9459i	−1.20406	−	1.65725i
$498$		0			0
$499$	−24.9700			−1.11781			−0.558906	−	0.829231i	$-0.688779\pi$
$499$	−24.9700			−1.11781			−0.558906	+	0.829231i	$0.688779\pi$
$500$		0			0
$501$	4.49299			0.200732
$502$		0			0
$503$	7.37458	+	10.1502i	0.328816	+	0.452576i	0.941133	−	0.338036i	$-0.109762\pi$
$503$	7.37458	+	10.1502i	0.328816	+	0.452576i	−0.612317	+	0.790612i	$0.709762\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			12.0663i			0.535885i
$508$		0			0
$509$	4.76735	−	14.6724i	0.211309	−	0.650342i	−0.788086	−	0.615565i	$-0.788928\pi$
$509$	4.76735	−	14.6724i	0.211309	−	0.650342i	0.999395	−	0.0347770i	$-0.0110721\pi$
$510$		0			0
$511$	0.285135	+	0.877556i	0.0126136	+	0.0388208i
$512$		0			0
$513$	−5.11572	−	1.66220i	−0.225865	−	0.0733878i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	3.11477	−	4.28711i	0.136987	−	0.188547i
$518$		0			0
$519$	−1.61654	−	1.17449i	−0.0709584	−	0.0515543i
$520$		0			0
$521$	15.6466	−	11.3679i	0.685490	−	0.498037i	−0.189685	−	0.981845i	$-0.560747\pi$
$521$	15.6466	−	11.3679i	0.685490	−	0.498037i	0.875174	+	0.483808i	$0.160747\pi$
$522$		0			0
$523$	6.61022	−	2.14779i	0.289045	−	0.0939163i	−0.160906	−	0.986970i	$-0.551442\pi$
$523$	6.61022	−	2.14779i	0.289045	−	0.0939163i	0.449951	+	0.893053i	$0.351442\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	18.7642	−	6.09686i	0.817382	−	0.265583i
$528$		0			0
$529$	−17.1151	+	12.4349i	−0.744136	+	0.540647i
$530$		0			0
$531$	5.89976	+	4.28642i	0.256028	+	0.186015i
$532$		0			0
$533$	−6.28244	+	8.64703i	−0.272123	+	0.374545i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−13.2951	−	4.31984i	−0.573727	−	0.186415i
$538$		0			0
$539$	−2.11259	−	6.50189i	−0.0909958	−	0.280056i
$540$		0			0
$541$	1.75145	−	5.39040i	0.0753006	−	0.231751i	−0.906321	−	0.422590i	$-0.861121\pi$
$541$	1.75145	−	5.39040i	0.0753006	−	0.231751i	0.981621	+	0.190839i	$0.0611209\pi$
$542$		0			0
$543$			13.5379i			0.580968i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−7.28835	−	10.0315i	−0.311627	−	0.428918i	0.624261	−	0.781216i	$-0.285400\pi$
$547$	−7.28835	−	10.0315i	−0.311627	−	0.428918i	−0.935888	+	0.352298i	$0.885400\pi$
$548$		0			0
$549$	4.81370			0.205444
$550$		0			0
$551$	3.79951			0.161865
$552$		0			0
$553$	−17.8586	−	24.5803i	−0.759427	−	1.04526i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			24.8970i			1.05492i	0.849579	+	0.527461i	$0.176856\pi$
$557$			24.8970i			1.05492i	−0.849579	+	0.527461i	$0.823144\pi$
$558$		0			0
$559$	2.09932	−	6.46105i	0.0887919	−	0.273273i
$560$		0			0
$561$	0.419687	+	1.29166i	0.0177192	+	0.0545340i
$562$		0			0
$563$	23.8035	+	7.73423i	1.00320	+	0.325959i	0.764143	−	0.645047i	$-0.223162\pi$
$563$	23.8035	+	7.73423i	1.00320	+	0.325959i	0.239055	+	0.971006i	$0.423162\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.54182	−	3.49851i	0.106746	−	0.146924i
$568$		0			0
$569$	1.69282	+	1.22991i	0.0709669	+	0.0515605i	0.622703	−	0.782458i	$-0.286034\pi$
$569$	1.69282	+	1.22991i	0.0709669	+	0.0515605i	−0.551736	+	0.834019i	$0.686034\pi$
$570$		0			0
$571$	9.32956	−	6.77832i	0.390430	−	0.283664i	−0.375202	−	0.926943i	$-0.622427\pi$
$571$	9.32956	−	6.77832i	0.390430	−	0.283664i	0.765632	+	0.643279i	$0.222427\pi$
$572$		0			0
$573$	−2.42089	+	0.786594i	−0.101134	+	0.0328604i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	5.55908	−	1.80625i	0.231427	−	0.0751954i	−0.191007	−	0.981589i	$-0.561175\pi$
$577$	5.55908	−	1.80625i	0.231427	−	0.0751954i	0.422435	+	0.906393i	$0.361175\pi$
$578$		0			0
$579$	−4.53487	+	3.29478i	−0.188463	+	0.136926i
$580$		0			0
$581$	−56.3655	−	40.9519i	−2.33843	−	1.69897i
$582$		0			0
$583$	−3.05858	+	4.20978i	−0.126673	+	0.174351i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−8.75234	−	2.84381i	−0.361248	−	0.117377i	0.122769	−	0.992435i	$-0.460823\pi$
$587$	−8.75234	−	2.84381i	−0.361248	−	0.117377i	−0.484017	+	0.875059i	$0.660823\pi$
$588$		0			0
$589$	14.1090	+	43.4231i	0.581352	+	1.78922i
$590$		0			0
$591$	2.42770	−	7.47170i	0.0998623	−	0.307345i
$592$		0			0
$593$			14.9033i			0.612004i	0.952031	+	0.306002i	$0.0989914\pi$
$593$			14.9033i			0.612004i	−0.952031	+	0.306002i	$0.901009\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	9.99060	+	13.7509i	0.408888	+	0.562786i
$598$		0			0
$599$	7.52244			0.307359			0.153679	−	0.988121i	$-0.450888\pi$
$599$	7.52244			0.307359			0.153679	+	0.988121i	$0.450888\pi$
$600$		0			0
$601$	18.6618			0.761232			0.380616	−	0.924733i	$-0.375712\pi$
$601$	18.6618			0.761232			0.380616	+	0.924733i	$0.375712\pi$
$602$		0			0
$603$	−0.221011	−	0.304195i	−0.00900025	−	0.0123878i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			0.810016i			0.0328776i	0.999865	+	0.0164388i	$0.00523286\pi$
$607$			0.810016i			0.0328776i	−0.999865	+	0.0164388i	$0.994767\pi$
$608$		0			0
$609$	−0.943920	+	2.90509i	−0.0382496	+	0.117720i
$610$		0			0
$611$	2.70802	+	8.33443i	0.109555	+	0.337175i
$612$		0			0
$613$	−4.74678	−	1.54232i	−0.191721	−	0.0622938i	0.211583	−	0.977360i	$-0.432138\pi$
$613$	−4.74678	−	1.54232i	−0.191721	−	0.0622938i	−0.403304	+	0.915066i	$0.632138\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−25.0455	+	34.4722i	−1.00829	+	1.38780i	−0.0881990	+	0.996103i	$0.528111\pi$
$617$	−25.0455	+	34.4722i	−1.00829	+	1.38780i	−0.920095	+	0.391695i	$0.871889\pi$
$618$		0			0
$619$	29.9038	+	21.7264i	1.20193	+	0.873257i	0.994474	−	0.104987i	$-0.0334800\pi$
$619$	29.9038	+	21.7264i	1.20193	+	0.873257i	0.207461	+	0.978243i	$0.433480\pi$
$620$		0			0
$621$	−1.09875	+	0.798291i	−0.0440915	+	0.0320343i
$622$		0			0
$623$	−57.6595	+	18.7347i	−2.31008	+	0.750590i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−2.98909	+	0.971215i	−0.119373	+	0.0387866i
$628$		0			0
$629$	11.5068	−	8.36018i	0.458806	−	0.333342i
$630$		0			0
$631$	26.8891	+	19.5361i	1.07044	+	0.777719i	0.975991	−	0.217811i	$-0.0698915\pi$
$631$	26.8891	+	19.5361i	1.07044	+	0.777719i	0.0944476	+	0.995530i	$0.469892\pi$
$632$		0			0
$633$	−7.61494	+	10.4811i	−0.302667	+	0.416585i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	10.7523	+	3.49364i	0.426022	+	0.138423i
$638$		0			0
$639$	−3.26336	−	10.0436i	−0.129097	−	0.397319i
$640$		0			0
$641$	−8.41649	+	25.9033i	−0.332431	+	1.02312i	0.635542	+	0.772066i	$0.280777\pi$
$641$	−8.41649	+	25.9033i	−0.332431	+	1.02312i	−0.967974	+	0.251052i	$0.919223\pi$
$642$		0			0
$643$			12.8557i			0.506978i	0.967338	+	0.253489i	$0.0815782\pi$
$643$			12.8557i			0.506978i	−0.967338	+	0.253489i	$0.918422\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.7155	−	25.7597i	−0.735784	−	1.01272i	−0.998850	−	0.0479418i	$-0.984734\pi$
$647$	−18.7155	−	25.7597i	−0.735784	−	1.01272i	0.263066	−	0.964778i	$-0.415266\pi$
$648$		0			0
$649$	4.26098			0.167258
$650$		0			0
$651$	−36.7062			−1.43863
$652$		0			0
$653$	−8.52402	−	11.7323i	−0.333571	−	0.459121i	0.608979	−	0.793186i	$-0.291579\pi$
$653$	−8.52402	−	11.7323i	−0.333571	−	0.459121i	−0.942550	+	0.334066i	$0.891579\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			0.213375i			0.00832454i
$658$		0			0
$659$	−10.2713	+	31.6118i	−0.400113	+	1.23142i	0.524795	+	0.851229i	$0.324142\pi$
$659$	−10.2713	+	31.6118i	−0.400113	+	1.23142i	−0.924908	+	0.380192i	$0.875858\pi$
$660$		0			0
$661$	−9.84316	−	30.2941i	−0.382854	−	1.17830i	−0.938025	−	0.346568i	$-0.887347\pi$
$661$	−9.84316	−	30.2941i	−0.382854	−	1.17830i	0.555170	−	0.831737i	$-0.312653\pi$
$662$		0			0
$663$	−2.13605	−	0.694044i	−0.0829573	−	0.0269545i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.563883	−	0.776118i	0.0218336	−	0.0300514i
$668$		0			0
$669$	−15.3552	−	11.1562i	−0.593668	−	0.431325i
$670$		0			0
$671$	2.27546	−	1.65322i	0.0878432	−	0.0638218i
$672$		0			0
$673$	−24.9095	+	8.09358i	−0.960190	+	0.311985i	−0.746849	−	0.664993i	$-0.768434\pi$
$673$	−24.9095	+	8.09358i	−0.960190	+	0.311985i	−0.213341	+	0.976978i	$0.568434\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.1177	−	4.58711i	0.542586	−	0.176297i	−0.0248849	−	0.999690i	$-0.507922\pi$
$677$	14.1177	−	4.58711i	0.542586	−	0.176297i	0.567471	+	0.823393i	$0.307922\pi$
$678$		0			0
$679$	55.1086	−	40.0387i	2.11487	−	1.53655i
$680$		0			0
$681$	−0.311560	−	0.226361i	−0.0119390	−	0.00867418i
$682$		0			0
$683$	3.30703	−	4.55174i	0.126540	−	0.174168i	−0.741046	−	0.671454i	$-0.765670\pi$
$683$	3.30703	−	4.55174i	0.126540	−	0.174168i	0.867586	+	0.497286i	$0.165670\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−9.76593	−	3.17314i	−0.372593	−	0.121063i
$688$		0			0
$689$	−2.65917	−	8.18408i	−0.101306	−	0.311788i
$690$		0			0
$691$	10.6330	−	32.7249i	0.404497	−	1.24492i	−0.516817	−	0.856096i	$-0.672883\pi$
$691$	10.6330	−	32.7249i	0.404497	−	1.24492i	0.921314	−	0.388819i	$-0.127117\pi$
$692$		0			0
$693$		−	2.52673i		−	0.0959824i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	15.1128	+	20.8009i	0.572436	+	0.787891i
$698$		0			0
$699$	−21.6380			−0.818425
$700$		0			0
$701$	8.86294			0.334749			0.167374	−	0.985893i	$-0.446471\pi$
$701$	8.86294			0.334749			0.167374	+	0.985893i	$0.446471\pi$
$702$		0			0
$703$	19.3466	+	26.6284i	0.729673	+	1.00431i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			30.8839i			1.16151i
$708$		0			0
$709$	−0.474877	+	1.46152i	−0.0178344	+	0.0548885i	−0.959578	−	0.281444i	$-0.909187\pi$
$709$	−0.474877	+	1.46152i	−0.0178344	+	0.0548885i	0.941743	+	0.336333i	$0.109187\pi$
$710$		0			0
$711$	−2.17113	−	6.68206i	−0.0814239	−	0.250597i
$712$		0			0
$713$	10.9638	+	3.56237i	0.410599	+	0.133412i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	4.53535	−	6.24238i	0.169376	−	0.233126i
$718$		0			0
$719$	−15.4808	−	11.2474i	−0.577335	−	0.419459i	0.260427	−	0.965493i	$-0.416137\pi$
$719$	−15.4808	−	11.2474i	−0.577335	−	0.419459i	−0.837762	+	0.546035i	$0.816137\pi$
$720$		0			0
$721$	−4.63740	+	3.36926i	−0.172706	+	0.125478i
$722$		0			0
$723$	24.0868	−	7.82629i	0.895799	−	0.291063i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−44.5184	+	14.4649i	−1.65110	+	0.536474i	−0.978977	−	0.203970i	$-0.934616\pi$
$727$	−44.5184	+	14.4649i	−1.65110	+	0.536474i	−0.672119	+	0.740443i	$0.734616\pi$
$728$		0			0
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	−13.2212	−	9.60574i	−0.489003	−	0.355281i
$732$		0			0
$733$	−29.9796	+	41.2634i	−1.10732	+	1.52410i	−0.282019	+	0.959409i	$0.591004\pi$
$733$	−29.9796	+	41.2634i	−1.10732	+	1.52410i	−0.825303	+	0.564690i	$0.808996\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.208946	−	0.0678906i	−0.00769662	−	0.00250078i
$738$		0			0
$739$	−4.08075	−	12.5592i	−0.150113	−	0.461999i	0.847520	−	0.530763i	$-0.178095\pi$
$739$	−4.08075	−	12.5592i	−0.150113	−	0.461999i	−0.997633	+	0.0687637i	$0.978095\pi$
$740$		0			0
$741$	1.60612	−	4.94312i	0.0590022	−	0.181590i
$742$		0			0
$743$		−	10.6063i		−	0.389107i	−0.980892	−	0.194553i	$-0.937674\pi$
$743$		−	10.6063i		−	0.389107i	0.980892	−	0.194553i	$-0.0623258\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−9.46998	−	13.0343i	−0.346488	−	0.476900i
$748$		0			0
$749$	−76.4534			−2.79355
$750$		0			0
$751$	28.2581			1.03115			0.515577	−	0.856843i	$-0.327578\pi$
$751$	28.2581			1.03115			0.515577	+	0.856843i	$0.327578\pi$
$752$		0			0
$753$	1.41018	+	1.94094i	0.0513897	+	0.0707318i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			27.7474i			1.00849i	0.863559	+	0.504247i	$0.168230\pi$
$757$			27.7474i			1.00849i	−0.863559	+	0.504247i	$0.831770\pi$
$758$		0			0
$759$	−0.245221	+	0.754713i	−0.00890096	+	0.0273943i
$760$		0			0
$761$	−4.97988	−	15.3265i	−0.180521	−	0.555585i	0.819322	−	0.573334i	$-0.194350\pi$
$761$	−4.97988	−	15.3265i	−0.180521	−	0.555585i	−0.999842	+	0.0177487i	$0.994350\pi$
$762$		0			0
$763$	−14.5582	−	4.73024i	−0.527042	−	0.171246i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.14181	+	5.70071i	−0.149552	+	0.205841i
$768$		0			0
$769$	−28.1081	−	20.4217i	−1.01360	−	0.736426i	−0.0486417	−	0.998816i	$-0.515489\pi$
$769$	−28.1081	−	20.4217i	−1.01360	−	0.736426i	−0.964962	+	0.262390i	$0.915489\pi$
$770$		0			0
$771$	−11.5759	+	8.41040i	−0.416897	+	0.302893i
$772$		0			0
$773$	22.3198	−	7.25215i	0.802788	−	0.260842i	0.121248	−	0.992622i	$-0.461310\pi$
$773$	22.3198	−	7.25215i	0.802788	−	0.260842i	0.681540	+	0.731781i	$0.261310\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−25.1662	+	8.17701i	−0.902834	+	0.293349i
$778$		0			0
$779$	−48.1363	+	34.9731i	−1.72466	+	1.25304i
$780$		0			0
$781$	−4.99199	−	3.62689i	−0.178627	−	0.129780i
$782$		0			0
$783$	−0.415189	+	0.571459i	−0.0148377	+	0.0204223i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−24.3677	−	7.91755i	−0.868615	−	0.282230i	−0.159393	−	0.987215i	$-0.550954\pi$
$787$	−24.3677	−	7.91755i	−0.868615	−	0.282230i	−0.709222	+	0.704985i	$0.750954\pi$
$788$		0			0
$789$	4.04210	+	12.4403i	0.143903	+	0.442887i
$790$		0			0
$791$	23.3696	−	71.9244i	0.830929	−	2.55734i
$792$		0			0
$793$			4.65129i			0.165172i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.13034	+	1.55577i	0.0400386	+	0.0551083i	0.828567	−	0.559890i	$-0.189157\pi$
$797$	1.13034	+	1.55577i	0.0400386	+	0.0551083i	−0.788528	+	0.614998i	$0.789157\pi$
$798$		0			0
$799$	21.0807			0.745781
$800$		0			0
$801$	−14.0197			−0.495362
$802$		0			0
$803$	0.0732815	+	0.100863i	0.00258605	+	0.00355939i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	30.6749i		−	1.07981i
$808$		0			0
$809$	14.0321	−	43.1862i	0.493341	−	1.51835i	−0.326185	−	0.945306i	$-0.605763\pi$
$809$	14.0321	−	43.1862i	0.493341	−	1.51835i	0.819526	−	0.573041i	$-0.194237\pi$
$810$		0			0
$811$	−7.39190	−	22.7499i	−0.259565	−	0.798858i	−0.992896	−	0.118987i	$-0.962035\pi$
$811$	−7.39190	−	22.7499i	−0.259565	−	0.798858i	0.733331	−	0.679872i	$-0.237965\pi$
$812$		0			0
$813$	13.5395	+	4.39924i	0.474850	+	0.154288i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	22.2291	−	30.5957i	0.777697	−	1.07041i
$818$		0			0
$819$	3.38048	+	2.45606i	0.118123	+	0.0858217i
$820$		0			0
$821$	25.5538	−	18.5659i	0.891834	−	0.647955i	−0.0445216	−	0.999008i	$-0.514176\pi$
$821$	25.5538	−	18.5659i	0.891834	−	0.647955i	0.936356	+	0.351053i	$0.114176\pi$
$822$		0			0
$823$	8.11491	−	2.63669i	0.282868	−	0.0919094i	−0.164147	−	0.986436i	$-0.552487\pi$
$823$	8.11491	−	2.63669i	0.282868	−	0.0919094i	0.447015	+	0.894527i	$0.352487\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−16.9224	+	5.49842i	−0.588450	+	0.191199i	−0.588082	−	0.808801i	$-0.700117\pi$
$827$	−16.9224	+	5.49842i	−0.588450	+	0.191199i	−0.000367397		1.00000i	$0.500117\pi$
$828$		0			0
$829$	−37.2323	+	27.0508i	−1.29313	+	0.939515i	−0.999864	−	0.0165158i	$-0.994743\pi$
$829$	−37.2323	+	27.0508i	−1.29313	+	0.939515i	−0.293267	+	0.956030i	$0.594743\pi$
$830$		0			0
$831$	16.2861	+	11.8325i	0.564957	+	0.410465i
$832$		0			0
$833$	15.9856	−	22.0023i	0.553869	−	0.762335i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−8.07273	−	2.62299i	−0.279034	−	0.0906637i
$838$		0			0
$839$	−0.312751	−	0.962548i	−0.0107974	−	0.0332308i	0.945513	−	0.325585i	$-0.105561\pi$
$839$	−0.312751	−	0.962548i	−0.0107974	−	0.0332308i	−0.956310	+	0.292354i	$0.905561\pi$
$840$		0			0
$841$	−8.80731	+	27.1061i	−0.303700	+	0.934694i
$842$		0			0
$843$		−	9.81651i		−	0.338099i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	27.0922	+	37.2892i	0.930899	+	1.28127i
$848$		0			0
$849$	6.54547			0.224640
$850$		0			0
$851$	8.31054			0.284882
$852$		0			0
$853$	−5.76813	−	7.93916i	−0.197497	−	0.271832i	0.698770	−	0.715347i	$-0.253731\pi$
$853$	−5.76813	−	7.93916i	−0.197497	−	0.271832i	−0.896267	+	0.443515i	$0.853731\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	57.3424i		−	1.95878i	−0.201979	−	0.979390i	$-0.564737\pi$
$857$		−	57.3424i		−	1.95878i	0.201979	−	0.979390i	$-0.435263\pi$
$858$		0			0
$859$	−3.31727	+	10.2095i	−0.113184	+	0.348344i	−0.991564	−	0.129619i	$-0.958625\pi$
$859$	−3.31727	+	10.2095i	−0.113184	+	0.348344i	0.878380	+	0.477963i	$0.158625\pi$
$860$		0			0
$861$	−14.7816	−	45.4932i	−0.503757	−	1.55040i
$862$		0			0
$863$	−9.16105	−	2.97661i	−0.311846	−	0.101325i	0.148913	−	0.988850i	$-0.452423\pi$
$863$	−9.16105	−	2.97661i	−0.311846	−	0.101325i	−0.460759	+	0.887525i	$0.652423\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	6.81665	−	9.38232i	0.231506	−	0.318640i
$868$		0			0
$869$	−3.32120	−	2.41299i	−0.112664	−	0.0818551i
$870$		0			0
$871$	0.293932	−	0.213554i	0.00995951	−	0.00723601i
$872$		0			0
$873$	14.9811	−	4.86764i	0.507032	−	0.164745i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.669370	−	0.217491i	0.0226030	−	0.00734416i	−0.297694	−	0.954661i	$-0.596217\pi$
$877$	0.669370	−	0.217491i	0.0226030	−	0.00734416i	0.320297	+	0.947317i	$0.396217\pi$
$878$		0			0
$879$	−0.703382	+	0.511037i	−0.0237245	+	0.0172369i
$880$		0			0
$881$	−8.03076	−	5.83469i	−0.270563	−	0.196576i	0.444228	−	0.895914i	$-0.353478\pi$
$881$	−8.03076	−	5.83469i	−0.270563	−	0.196576i	−0.714791	+	0.699338i	$0.753478\pi$
$882$		0			0
$883$	−9.89850	+	13.6241i	−0.333111	+	0.458488i	−0.942414	−	0.334450i	$-0.891450\pi$
$883$	−9.89850	+	13.6241i	−0.333111	+	0.458488i	0.609302	+	0.792938i	$0.291450\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	44.1212	+	14.3358i	1.48144	+	0.481351i	0.934544	−	0.355847i	$-0.115808\pi$
$887$	44.1212	+	14.3358i	1.48144	+	0.481351i	0.546901	+	0.837198i	$0.315808\pi$
$888$		0			0
$889$	−23.3935	−	71.9979i	−0.784594	−	2.41473i
$890$		0			0
$891$	0.180557	−	0.555698i	0.00604890	−	0.0186166i
$892$		0			0
$893$			48.7837i			1.63249i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.771358	−	1.06168i	−0.0257549	−	0.0354486i
$898$		0			0
$899$	5.99572			0.199968
$900$		0			0
$901$	−20.7004			−0.689630
$902$		0			0
$903$	17.8709	+	24.5972i	0.594706	+	0.818543i
$904$		0			0
$905$		0			0
$906$		0			0
$907$			28.5101i			0.946662i	0.880885	+	0.473331i	$0.156949\pi$
$907$			28.5101i			0.946662i	−0.880885	+	0.473331i	$0.843051\pi$
$908$		0			0
$909$	−2.20693	+	6.79224i	−0.0731993	+	0.225284i
$910$		0			0
$911$	−2.00884	−	6.18256i	−0.0665557	−	0.204837i	0.912248	−	0.409639i	$-0.134345\pi$
$911$	−2.00884	−	6.18256i	−0.0665557	−	0.204837i	−0.978804	+	0.204801i	$0.934345\pi$
$912$		0			0
$913$	−8.95301	−	2.90901i	−0.296301	−	0.0962742i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−47.9539	+	66.0029i	−1.58358	+	2.17961i
$918$		0			0
$919$	13.6130	+	9.89041i	0.449051	+	0.326255i	0.789221	−	0.614109i	$-0.210485\pi$
$919$	13.6130	+	9.89041i	0.449051	+	0.326255i	−0.340170	+	0.940364i	$0.610485\pi$
$920$		0			0
$921$	17.5768	−	12.7703i	0.579174	−	0.420795i
$922$		0			0
$923$	9.70474	−	3.15326i	0.319436	−	0.103791i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1.26066	+	0.409613i	−0.0414054	+	0.0134534i
$928$		0			0
$929$	−25.5979	+	18.5979i	−0.839839	+	0.610179i	−0.922326	−	0.386413i	$-0.873714\pi$
$929$	−25.5979	+	18.5979i	−0.839839	+	0.610179i	0.0824866	+	0.996592i	$0.473714\pi$
$930$		0			0
$931$	50.9165	+	36.9930i	1.66872	+	1.21240i
$932$		0			0
$933$	11.1580	−	15.3576i	0.365296	−	0.502787i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−2.23598	−	0.726513i	−0.0730462	−	0.0237341i	0.272266	−	0.962222i	$-0.412227\pi$
$937$	−2.23598	−	0.726513i	−0.0730462	−	0.0237341i	−0.345312	+	0.938488i	$0.612227\pi$
$938$		0			0
$939$	−1.87947	−	5.78443i	−0.0613343	−	0.188768i
$940$		0			0
$941$	1.32816	−	4.08766i	0.0432968	−	0.133254i	−0.927071	−	0.374885i	$-0.877682\pi$
$941$	1.32816	−	4.08766i	0.0432968	−	0.133254i	0.970368	+	0.241631i	$0.0776823\pi$
$942$		0			0
$943$			15.0230i			0.489217i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−16.3650	−	22.5245i	−0.531791	−	0.731948i	0.455611	−	0.890179i	$-0.349421\pi$
$947$	−16.3650	−	22.5245i	−0.531791	−	0.731948i	−0.987402	+	0.158231i	$0.949421\pi$
$948$		0			0
$949$	−0.206176			−0.00669275
$950$		0			0
$951$	−1.97817			−0.0641467
$952$		0			0
$953$	−26.2275	−	36.0991i	−0.849593	−	1.16936i	−0.983952	−	0.178432i	$-0.942898\pi$
$953$	−26.2275	−	36.0991i	−0.849593	−	1.16936i	0.134359	−	0.990933i	$-0.457102\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			0.412724i			0.0133415i
$958$		0			0
$959$	−17.7072	+	54.4971i	−0.571795	+	1.75980i
$960$		0			0
$961$	12.6848	+	39.0399i	0.409188	+	1.25935i
$962$		0			0
$963$	−16.8143	−	5.46328i	−0.541832	−	0.176052i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−32.4372	+	44.6460i	−1.04311	+	1.43572i	−0.148479	+	0.988916i	$0.547438\pi$
$967$	−32.4372	+	44.6460i	−1.04311	+	1.43572i	−0.894632	+	0.446804i	$0.852562\pi$
$968$		0			0
$969$	−10.1151	−	7.34902i	−0.324942	−	0.236084i
$970$		0			0
$971$	5.00915	−	3.63936i	0.160751	−	0.116793i	−0.504502	−	0.863411i	$-0.668324\pi$
$971$	5.00915	−	3.63936i	0.160751	−	0.116793i	0.665253	+	0.746618i	$0.268324\pi$
$972$		0			0
$973$	−69.5160	+	22.5871i	−2.22858	+	0.724109i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−22.9819	+	7.46728i	−0.735257	+	0.238900i	−0.652626	−	0.757681i	$-0.726333\pi$
$977$	−22.9819	+	7.46728i	−0.735257	+	0.238900i	−0.0826317	+	0.996580i	$0.526333\pi$
$978$		0			0
$979$	−6.62719	+	4.81494i	−0.211806	+	0.153886i
$980$		0			0
$981$	−2.86374	−	2.08063i	−0.0914321	−	0.0664293i
$982$		0			0
$983$	5.59750	−	7.70430i	0.178533	−	0.245729i	−0.710367	−	0.703832i	$-0.751471\pi$
$983$	5.59750	−	7.70430i	0.178533	−	0.245729i	0.888899	+	0.458103i	$0.151471\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−37.2998	−	12.1194i	−1.18727	−	0.385766i
$988$		0			0
$989$	−2.95072	−	9.08137i	−0.0938273	−	0.288771i
$990$		0			0
$991$	−3.21741	+	9.90216i	−0.102204	+	0.314553i	−0.989064	−	0.147486i	$-0.952882\pi$
$991$	−3.21741	+	9.90216i	−0.102204	+	0.314553i	0.886860	+	0.462039i	$0.152882\pi$
$992$		0			0
$993$		−	13.1307i		−	0.416691i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	33.9556	+	46.7359i	1.07539	+	1.48014i	0.864502	+	0.502629i	$0.167634\pi$
$997$	33.9556	+	46.7359i	1.07539	+	1.48014i	0.210883	+	0.977511i	$0.432366\pi$
$998$		0			0
$999$	−6.11909			−0.193599

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.o.b.349.2		16
5.2	odd	4		1500.2.m.a.901.1		8
5.3	odd	4		300.2.m.b.181.1	yes	8
5.4	even	2	inner	1500.2.o.b.349.3		16
15.8	even	4		900.2.n.b.181.2		8
25.2	odd	20		7500.2.a.f.1.1		4
25.3	odd	20		300.2.m.b.121.1	✓	8
25.4	even	10	inner	1500.2.o.b.649.1		16
25.11	even	5		7500.2.d.c.1249.8		8
25.14	even	10		7500.2.d.c.1249.1		8
25.21	even	5	inner	1500.2.o.b.649.4		16
25.22	odd	20		1500.2.m.a.601.1		8
25.23	odd	20		7500.2.a.e.1.4		4
75.53	even	20		900.2.n.b.721.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.b.121.1	✓	8	25.3	odd	20
300.2.m.b.181.1	yes	8	5.3	odd	4
900.2.n.b.181.2		8	15.8	even	4
900.2.n.b.721.2		8	75.53	even	20
1500.2.m.a.601.1		8	25.22	odd	20
1500.2.m.a.901.1		8	5.2	odd	4
1500.2.o.b.349.2		16	1.1	even	1	trivial
1500.2.o.b.349.3		16	5.4	even	2	inner
1500.2.o.b.649.1		16	25.4	even	10	inner
1500.2.o.b.649.4		16	25.21	even	5	inner
7500.2.a.e.1.4		4	25.23	odd	20
7500.2.a.f.1.1		4	25.2	odd	20
7500.2.d.c.1249.1		8	25.14	even	10
7500.2.d.c.1249.8		8	25.11	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{3} +4.32440i q^{7} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{3} +4.32440i q^{7} +(-0.309017 + 0.951057i) q^{9} +(0.180557 + 0.555698i) q^{11} +(-0.918969 - 0.298591i) q^{13} +(-1.36625 + 1.88048i) q^{17} +(-4.35169 - 3.16169i) q^{19} +(3.49851 - 2.54182i) q^{21} +(-1.29166 + 0.419687i) q^{23} +(0.951057 - 0.309017i) q^{27} +(-0.571459 + 0.415189i) q^{29} +(-6.86707 - 4.98922i) q^{31} +(0.343440 - 0.472705i) q^{33} +(-5.81960 - 1.89090i) q^{37} +(0.298591 + 0.918969i) q^{39} +(3.41820 - 10.5201i) q^{41} +7.03076i q^{43} +(-5.33081 - 7.33723i) q^{47} -11.7004 q^{49} +2.32440 q^{51} +(5.23465 + 7.20487i) q^{53} +5.37899i q^{57} +(2.25351 - 6.93558i) q^{59} +(-1.48752 - 4.57810i) q^{61} +(-4.11275 - 1.33631i) q^{63} +(-0.221011 + 0.304195i) q^{67} +(1.09875 + 0.798291i) q^{69} +(-8.54359 + 6.20729i) q^{71} +(0.202931 - 0.0659364i) q^{73} +(-2.40306 + 0.780801i) q^{77} +(-5.68410 + 4.12974i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-9.46998 + 13.0343i) q^{83} +(0.671790 + 0.218278i) q^{87} +(4.33233 + 13.3335i) q^{89} +(1.29123 - 3.97399i) q^{91} +8.48817i q^{93} +(-9.25880 - 12.7436i) q^{97} -0.584296 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^9	\( 16 q + 4 q^{9} + 16 q^{11} - 10 q^{19} + 14 q^{21} + 6 q^{29} - 6 q^{31} + 20 q^{41} + 16 q^{49} - 16 q^{51} + 76 q^{59} + 92 q^{61} - 4 q^{69} - 50 q^{71} + 32 q^{79} - 4 q^{81} + 60 q^{89} + 50 q^{91} + 4 q^{99}+O(q^{100}) \) 16 * q + 4 * q^9 + 16 * q^11 - 10 * q^19 + 14 * q^21 + 6 * q^29 - 6 * q^31 + 20 * q^41 + 16 * q^49 - 16 * q^51 + 76 * q^59 + 92 * q^61 - 4 * q^69 - 50 * q^71 + 32 * q^79 - 4 * q^81 + 60 * q^89 + 50 * q^91 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more